Finite Group Databasebeta

← #6500775

Subgroups — #6500775

Order 512.

2474 conjugacy classes of subgroups.

The subgroup lattice has 895 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35512C211yesmaximal, characteristic
2#34361C211yesmaximal, characteristic, complemented
3#27597C211yesmaximal, characteristic, complemented
4#27595C211yesmaximal, characteristic, complemented
5#27591C211yesmaximal, characteristic, complemented
6#27591C211yesmaximal, characteristic, complemented
7#24891C212yesmaximal, complemented
8#24890C212yesmaximal, complemented
9#24887C212yesmaximal, complemented
10#24886C212yesmaximal, complemented
11#24874C212yesmaximal, complemented
12#24873C212yesmaximal, complemented
13#24870C212yesmaximal, complemented
14#24869C212yesmaximal, complemented
15#24009C212yesmaximal, complemented
16#24008C212yesmaximal, complemented
17#21945C212yesmaximal, complemented
18#21744C211yesmaximal, characteristic, complemented
19#20602C212yesmaximal, complemented
20C22×H(5,𝔽2)C2211yescharacteristic
21C2×#525C2211yescharacteristic
22C2×#525C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C2×#485C2212yescomplemented
25C2×#482C2212yescomplemented
26C2×#482C2212yescomplemented
27C2×#482C2212yescomplemented
28C2×#417C2212yescomplemented
29C2×#418C2212yescomplemented
30C2×#416C2212yescomplemented
31C22×#102C2212yescomplemented
32C2×#408C2212yes—
33#2408—22no—
34#2408C2212yes—
35#2408C2212yes—
36#2407—22no—
37#2407C2212yes—
38#2407C2212yes—
39#2405—22no—
40#2403—22no—
41#2375—22no—
42#2374—22no—
43#2354C2212yescomplemented
44#2354C2212yescomplemented
45#2352C2212yescomplemented
46#2352C2212yescomplemented
47#2333—22no—
48#2332—22no—
49#2314C2211yescharacteristic, complemented
50#2314C2211yescharacteristic, complemented
51#2311C2211yescharacteristic
52#2311C2212yes—
53#2311C2211yescharacteristic
54#2309C2211yescharacteristic
55#2280C2212yescomplemented
56#2096C2211yescharacteristic, complemented
57#2095C2211yescharacteristic, complemented
58#2094C2211yescharacteristic, complemented
59#2093C2211yescharacteristic, complemented
60#2092C2212yescomplemented
61#2092C2212yescomplemented
62#2074C2211yescharacteristic, complemented
63#2074C2211yescharacteristic, complemented
64#2073C2211yescharacteristic, complemented
65#2073C2211yescharacteristic, complemented
66#2071C2212yescomplemented
67#2071C2212yescomplemented
68#2036C2212yescomplemented
69#2035C2212yescomplemented
70#2034C2212yescomplemented
71#2034C2212yescomplemented
72#2034C2212yescomplemented
73#2033C2212yescomplemented
74#2033C2212yescomplemented
75#2033C2212yescomplemented
76#1928C2212yescomplemented
77#1927C2212yescomplemented
78#1926C2212yescomplemented
79#1926C2212yescomplemented
80#1926C2212yescomplemented
81#1925C2212yescomplemented
82#1925C2212yescomplemented
83#1925C2212yescomplemented
84#1875C2212yescomplemented
85#1875C2212yescomplemented
86#1875C2212yescomplemented
87#1873C2212yescomplemented
88#1870C2212yescomplemented
89#1870C2212yescomplemented
90#1869C2212yescomplemented
91#1869C2212yescomplemented
92#1854C2212yescomplemented
93#1854C2212yescomplemented
94#1854C2212yescomplemented
95#1854C2212yescomplemented
96#1853C2212yescomplemented
97#1853C2212yescomplemented
98#1852C2212yescomplemented
99#1852C2212yescomplemented
100#1818C2211yescharacteristic, complemented
101#1818C2211yescharacteristic, complemented
102#1809C2212yescomplemented
103#1809C2212yescomplemented
104#1808C2212yescomplemented
105#1807C2212yescomplemented
106#1788C2212yes—
107#1788C2212yes—
108#1788C2212yescomplemented
109#1788C2212yescomplemented
110#1786C2212yes—
111#1786C2212yes—
112#1786C2212yescomplemented
113#1786C2212yescomplemented
114#1779C2212yescomplemented
115C2×H(5,𝔽2)—28no—
116C2×H(5,𝔽2)—42no—
117C2×H(5,𝔽2)—44no—
118C2×H(5,𝔽2)—42no—
119C22×#41—21no—
120C22×#41C2311yescharacteristic
121C22×#41C2312yes—
122C22×#41C2311yescharacteristic
123C23×D4—21no—
124C23×D4—22no—
125C23×D4—21no—
126C23×D4C2311yescharacteristic
127C23×D4C2312yes—
128C24×C4C2311yescharacteristic
129C22×M16C2312yes—
130C23×C8C2312yes—
131#525—28no—
132#525—42no—
133#525—42no—
134C2×#123—21no—
135C2×#123D412yes—
136C2×C22⋊Q8D412yes—
137C2×C22⋊Q8C2312yes—
138C2×#121—22no—
139C2×#121—44no—
140C2×#121D412yes—
141C2×#121C2312yes—
142C2×#121C2312yes—
143C2×#121C2312yes—
144C2×#120—21no—
145C2×#120—22no—
146C2×#120—22no—
147C2×#120D412yes—
148C2×C4×D4—22no—
149C2×C4×D4C2312yes—
150C2×C4×D4C2312yes—
151C2×#117C2311yescharacteristic
152C2×#117C2312yes—
153C2×#117C2312yes—
154C2×#117C2312yes—
155C2×#117C2311yescharacteristic
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2312yes—
158C22×C22⋊C4—21no—
159#485—44no—
160#482—44no—
161#482—44no—
162#482—44no—
163C2×#107C2312yes—
164C2×#107C2312yes—
165C2×#107C2312yes—
166C2×#107C2312yes—
167C2×#106C2312yes—
168C2×#106C2312yes—
169C2×#106C2312yes—
170C2×#106C2312yes—
171#418—44no—
172#417—44no—
173#416—44no—
174C2×#103C2312yes—
175C2×#103C2312yes—
176C2×#103C2312yes—
177C2×#103C2312yes—
178C2×#102—44no—
179C2×#102C2312yes—
180C2×#102C2312yes—
181C2×#102C2312yes—
182C2×#102C2312yes—
183C2×#102C2312yes—
184C2×#102C2312yes—
185C2×#102C2312yes—
186C2×#102C2312yes—
187C2×#102C2312yes—
188C2×#102C2312yes—
189C2×#102C2312yes—
190C2×#102C2312yes—
191#408—28no—
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2312yes—
196C2×C22⋊C8C2312yes—
197C2×C22⋊C8C2312yes—
198C2×C22⋊C8C2312yes—
199C2×C22⋊C8C2312yes—
200#394—22no—
201#394—22no—
202#394—22no—
203#394—22no—
204#392—22no—
205#392—22no—
206#392—22no—
207#392—22no—
208#391—22no—
209#391—21no—
210#391C2311yescharacteristic
211#391C2311yescharacteristic
212#390—22no—
213#390—21no—
214#390—22no—
215#390—22no—
216#390—22no—
217#390C2312yes—
218#390C2312yes—
219#390C2311yescharacteristic
220#390C2311yescharacteristic
221#388—22no—
222#388—22no—
223#388—22no—
224#388—22no—
225#388—22no—
226#388—22no—
227#388—22no—
228#388—22no—
229#387—22no—
230#387—22no—
231#387—22no—
232#387—22no—
233#386—22no—
234#386—22no—
235#386—22no—
236#386—22no—
237#386—22no—
238#386—22no—
239#386—22no—
240#386—22no—
241#385—22no—
242#385—22no—
243#384C2311yescharacteristic
244#384C2311yescharacteristic
245#382C2311yescharacteristic
246#382C2311yescharacteristic
247#381—22no—
248#380—22no—
249#380C2312yes—
250#380C2312yes—
251#380C2312yes—
252#380C2312yes—
253#380C2312yes—
254#380C2312yes—
255#380C2312yes—
256#380C2312yes—
257#379—22no—
258#379—22no—
259#379—22no—
260#379—22no—
261C4×C4⋊C4—22no—
262C4×C4⋊C4—22no—
263C4×C4⋊C4C2312yes—
264C4×C4⋊C4C2312yes—
265C4×C22⋊C4—22no—
266C4×C22⋊C4—22no—
267C4×C22⋊C4—22no—
268C4×C22⋊C4—22no—
269#340C2312yes—
270#340C2312yes—
271#340C2312yes—
272#340C2312yes—
273#340C2312yes—
274#340C2312yes—
275#340C2312yes—
276#340C2312yes—
277#336C2312yes—
278#336C2312yes—
279#336C2311yescharacteristic
280#336C2311yescharacteristic
281#336C2311yescharacteristic
282#336C2311yescharacteristic
283C25—21no—
284C25—22no—
285C25C2×D411yescharacteristic
286H(5,𝔽2)—432no—
287H(5,𝔽2)—432no—
288C2×#41—22no—
289C2×#41—22no—
290C2×#41—24no—
291C2×#41—24no—
292C2×#41—24no—
293C2×#41—24no—
294C2×#41—24no—
295C2×#41—41no—
296C2×#41—41no—
297C2×#41—42no—
298C2×#41—42no—
299C2×#41—42no—
300C2×#41—42no—
301C2×#41—44no—
302C2×#41—44no—
303C2×#41—44no—
304C2×#41#4118yes—
305C22×Q8C2×D411yescharacteristic
306C22×Q8C2411yescharacteristic
307C22×D4—24no—
308C22×D4—24no—
309C22×D4—21no—
310C22×D4—24no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4—21no—
316C22×D4—22no—
317C22×D4—24no—
318C22×D4—24no—
319C22×D4—24no—
320C22×D4—42no—
321C22×D4—42no—
322C22×D4—41no—
323C22×D4—41no—
324C22×D4—44no—
325C22×D4—48no—
326C22×D4—44no—
327C22×D4—48no—
328C22×D4—48no—
329C22×D4—44no—
330C22×D4—44no—
331C22×D4—84no—
332C22×D4C2×D412yes—
333C22×D4C2×D412yes—
334C22×D4C2×D412yes—
335C22×D4C2×D411yescharacteristic
336C22×D4C2411yescharacteristic
337C22×D4C2412yes—
338C23×C4—21no—
339C23×C4—24no—
340C23×C4—21no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—42no—
344C23×C4—41no—
345C23×C4—41no—
346C23×C4C2×D411yescharacteristic
347C23×C4C2×D412yes—
348C23×C4C2412yes—
349C23×C4C2411yescharacteristic
350C23×C4C2412yes—
351C2×M16—24no—
352C2×M16—42no—
353C2×M16—42no—
354C22×C8—24no—
355C22×C8—42no—
356C22×C8—42no—
357C22×C8C2412yes—
358C22×C8C2412yes—
359C22×C8C2412yes—
360C22×C8C2412yes—
361#123—28no—
362#123—44no—
363C22⋊Q8—28no—
364C22⋊Q8—24no—
365C22⋊Q8—42no—
366#121—28no—
367#121—24no—
368#121—24no—
369#121—24no—
370#121—42no—
371#121—42no—
372#121—42no—
373#121—48no—
374#120—28no—
375#120—44no—
376#120—84no—
377#120—84no—
378C4×D4—24no—
379C4×D4—24no—
380C4×D4—24no—
381C4×D4—24no—
382C4×D4—48no—
383#117—24no—
384#117—41no—
385#117—41no—
386#117—42no—
387#117—42no—
388#117—42no—
389#117—42no—
390#117—42no—
391#117—42no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—42no—
398C2×C4⋊C4—42no—
399C2×C4⋊C4—42no—
400C2×C4⋊C4C2×D412yes—
401C2×C4⋊C4C2×D412yes—
402C2×C4⋊C4C2×D412yes—
403C2×C4⋊C4C2412yes—
404C2×C4⋊C4C2412yes—
405C2×C4⋊C4C2411yescharacteristic
406C2×C4⋊C4C2411yescharacteristic
407C2×C4⋊C4C2412yes—
408C2×C4⋊C4C2412yes—
409C2×C4⋊C4C2412yes—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—44no—
433C2×C22⋊C4C2×D412yes—
434C2×C22⋊C4C2×D412yes—
435C2×C22⋊C4C2×D412yes—
436C2×C22⋊C4C2×D412yes—
437C2×C22⋊C4C2×D412yes—
438C2×C42—21no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42C2411yescharacteristic
445C2×C42C2411yescharacteristic
446#107—42no—
447#107—42no—
448#107—42no—
449#107—42no—
450#106—42no—
451#106—42no—
452#106—42no—
453#106—42no—
454#103—24no—
455#103—24no—
456#103—42no—
457#103—42no—
458#102—24no—
459#102—24no—
460#102—24no—
461#102—24no—
462#102—24no—
463#102—24no—
464#102—42no—
465#102—42no—
466#102—42no—
467#102—42no—
468#102—42no—
469#102—42no—
470C22⋊C8—24no—
471C22⋊C8—24no—
472C22⋊C8—24no—
473C22⋊C8—24no—
474C22⋊C8—42no—
475C22⋊C8—42no—
476C22⋊C8—42no—
477C22⋊C8—42no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488#95—22no—
489#95—22no—
490#95—22no—
491#95—22no—
492C24—24no—
493C24—21no—
494C24—22no—
495C24—22no—
496C24—41no—
497C24—42no—
498C24—41no—
499C24—42no—
500C24—44no—
501C24—44no—
502C24—42no—
503C24—44no—
504C24—42no—
505C24—82no—
506C24—82no—
507C24—82no—
508C24—82no—
509C24—82no—
510C24—82no—
511C24C22×D412yes—
512C24C22×D411yescharacteristic
513C24C22×D412yes—
514#41—216no—
515#41—48no—
516#41—48no—
517#41—48no—
518#41—48no—
519#41—48no—
520#41—48no—
521#41—48no—
522#41—432no—
523C2×Q8—21no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—41no—
527C2×Q8—41no—
528C2×Q8#12314yes—
529C2×Q8H(5,𝔽2)12yes—
530C2×D4—216no—
531C2×D4—24no—
532C2×D4—24no—
533C2×D4—24no—
534C2×D4—24no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—21no—
543C2×D4—48no—
544C2×D4—48no—
545C2×D4—48no—
546C2×D4—48no—
547C2×D4—41no—
548C2×D4—42no—
549C2×D4—41no—
550C2×D4—42no—
551C2×D4—44no—
552C2×D4—44no—
553C2×D4—44no—
554C2×D4—42no—
555C2×D4—48no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—44no—
561C2×D4—42no—
562C2×D4—432no—
563C2×D4—464no—
564C2×D4—42no—
565C2×D4—44no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—42no—
574C2×D4—82no—
575C2×D4—82no—
576C2×D4—82no—
577C2×D4—816no—
578C2×D4#12318yes—
579C2×D4#12314yes—
580C2×D4H(5,𝔽2)12yes—
581C2×D4H(5,𝔽2)14yes—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—24no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—24no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—44no—
607C22×C4—41no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—41no—
611C22×C4—44no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—44no—
615C22×C4—42no—
616C22×C4—84no—
617C22×C4—84no—
618C22×C4—82no—
619C22×C4—82no—
620C22×C4—82no—
621C22×C4—82no—
622C22×C4C22×D412yes—
623C22×C4C22×D412yes—
624C22×C4C22×D412yes—
625C22×C4C22×D412yes—
626C22×C4C22×D411yescharacteristic
627C22×C4C2×#4114yes—
628C22×C4C2×#4114yes—
629C22×C4C2×#4114yes—
630C22×C4C2511yescharacteristic
631M16—84no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—84no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—44no—
661C4⋊C4—42no—
662C4⋊C4—82no—
663C4⋊C4—82no—
664C4⋊C4—82no—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—44no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—42no—
675C22⋊C4—82no—
676C22⋊C4—82no—
677C22⋊C4—82no—
678C22⋊C4—82no—
679C22⋊C4—82no—
680C22⋊C4—82no—
681C22⋊C4—82no—
682C22⋊C4—82no—
683C22⋊C4—82no—
684C22⋊C4—82no—
685C22⋊C4—82no—
686C22⋊C4—82no—
687C22⋊C4—82no—
688C22⋊C4—82no—
689C22⋊C4—82no—
690C22⋊C4—82no—
691C22⋊C4—82no—
692C42—22no—
693C42—22no—
694C42—42no—
695C42—82no—
696C42—82no—
697C42—82no—
698C42—82no—
699C42—82no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—21no—
707C23—22no—
708C23—21no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—24no—
718C23—22no—
719C23—416no—
720C23—48no—
721C23—44no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—41no—
729C23—42no—
730C23—42no—
731C23—41no—
732C23—82no—
733C23—84no—
734C23—84no—
735C23—82no—
736C23—84no—
737C23—84no—
738C23—164no—
739C23—164no—
740C23—164no—
741C23—164no—
742C23—164no—
743C23—164no—
744C23—164no—
745C23—164no—
746C23C2×#12312yes—
747C23C2×#12314yes—
748C23C23×D411yescharacteristic
749Q8—24no—
750Q8—44no—
751Q8—42no—
752D4—24no—
753D4—24no—
754D4—24no—
755D4—44no—
756D4—48no—
757D4—48no—
758D4—416no—
759D4—48no—
760D4—416no—
761D4—42no—
762D4—42no—
763D4—42no—
764D4—84no—
765D4—84no—
766D4—88no—
767D4—88no—
768D4—88no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—48no—
790C2×C4—416no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—84no—
817C2×C4—82no—
818C2×C4—84no—
819C2×C4—164no—
820C2×C4C2×#12314yes—
821C2×C4C2×#12312yes—
822C2×C4C22×#4112yes—
823C2×C4C2×H(5,𝔽2)11yescharacteristic
824C2×C4C2×H(5,𝔽2)11yescharacteristic
825C2×C4C2×H(5,𝔽2)12yes—
826C8—42no—
827C8—42no—
828C8—42no—
829C8—42no—
830C22—22no—
831C22—24no—
832C22—24no—
833C22—24no—
834C22—24no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—41no—
839C22—42no—
840C22—41no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—44no—
849C22—42no—
850C22—42no—
851C22—44no—
852C22—42no—
853C22—44no—
854C22—88no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22—81no—
861C22—81no—
862C22—168no—
863C22—1616no—
864C22C22×#12311yescharacteristic
865C22#348411yescharacteristic
866C22#348411yescharacteristic
867C22#358412yes—
868C22#358512yes—
869C4—22no—
870C4—24no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—42no—
875C4—82no—
876C4—82no—
877C4—82no—
878C4—82no—
879C4—82no—
880C4—81no—
881C4—81no—
882C4#349012yes—
883C4#349012yes—
884C2—42no—
885C2—44no—
886C2—82no—
887C2—82no—
888C2—84no—
889C2#3535011yescharacteristic
890C2#6052312yes—
891C2#6162512yes—
892C2#6163511yescharacteristic
893C2#6164311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35512C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#525 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #34361C2semidirect
3. #27597C2semidirect
4. #27595C2semidirect
5. #27591C2semidirect
6. #27591C2semidirect
7. #24891C2semidirect
8. #24890C2semidirect
9. #24887C2semidirect
10. #24886C2semidirect
11. #24874C2semidirect
12. #24873C2semidirect
13. #24870C2semidirect
14. #24869C2semidirect
15. #24009C2semidirect
16. #24008C2semidirect
17. #21945C2semidirect
18. #21744C2semidirect
19. #20602C2semidirect
24. C2×#485C22semidirect
25. C2×#482C22semidirect
26. C2×#482C22semidirect
27. C2×#482C22semidirect
28. C2×#417C22semidirect
29. C2×#418C22semidirect
30. C2×#416C22semidirect
31. C22×#102C22semidirect
43. #2354C22semidirect
44. #2354C22semidirect
45. #2352C22semidirect
46. #2352C22semidirect
49. #2314C22semidirect
50. #2314C22semidirect
55. #2280C22semidirect
56. #2096C22semidirect
57. #2095C22semidirect
58. #2094C22semidirect
59. #2093C22semidirect
60. #2092C22semidirect
61. #2092C22semidirect
62. #2074C22semidirect
63. #2074C22semidirect
64. #2073C22semidirect
65. #2073C22semidirect
66. #2071C22semidirect
67. #2071C22semidirect
68. #2036C22semidirect
69. #2035C22semidirect
70. #2034C22semidirect
71. #2034C22semidirect
72. #2034C22semidirect
73. #2033C22semidirect
74. #2033C22semidirect
75. #2033C22semidirect
76. #1928C22semidirect
77. #1927C22semidirect
78. #1926C22semidirect
79. #1926C22semidirect
80. #1926C22semidirect
81. #1925C22semidirect
82. #1925C22semidirect
83. #1925C22semidirect
84. #1875C22semidirect
85. #1875C22semidirect
86. #1875C22semidirect
87. #1873C22semidirect
88. #1870C22semidirect
89. #1870C22semidirect
90. #1869C22semidirect
91. #1869C22semidirect
92. #1854C22semidirect
93. #1854C22semidirect
94. #1854C22semidirect
95. #1854C22semidirect
96. #1853C22semidirect
97. #1853C22semidirect
98. #1852C22semidirect
99. #1852C22semidirect
100. #1818C22semidirect
101. #1818C22semidirect
102. #1809C22semidirect
103. #1809C22semidirect
104. #1808C22semidirect
105. #1807C22semidirect
108. #1788C22semidirect
109. #1788C22semidirect
112. #1786C22semidirect
113. #1786C22semidirect
114. #1779C22semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#355122
#343612
#275972
#275952
#275912
#248912
#248902
#248872
#248862
#248742
#248732
#248702
#248692
#240092
#240082
#219452
#217442
#206022